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Mirrors > Home > MPE Home > Th. List > equs4 | Structured version Visualization version Unicode version |
Description: Lemma used in proofs of implicit substitution properties. The converse requires either a dv condition (sb56 2082) or a non-freeness hypothesis (equs45f 2182). See equs4v 1850 for a version requiring fewer axioms. (Contributed by NM, 10-May-1993.) (Proof shortened by Mario Carneiro, 20-May-2014.) (Proof shortened by Wolf Lammen, 5-Feb-2018.) |
Ref | Expression |
---|---|
equs4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6e 2095 |
. 2
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2 | exintr 1760 |
. 2
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3 | 1, 2 | mpi 20 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-12 1937 ax-13 2092 |
This theorem depends on definitions: df-bi 190 df-an 377 df-ex 1668 |
This theorem is referenced by: equsex 2131 equs45f 2182 equs5 2183 sb2 2184 |
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