Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > gen12 | Structured version Visualization version GIF version |
Description: Virtual deduction generalizing rule for two quantifying variables and one virtual hypothesis. gen12 37864 is alrimivv 1843 with virtual deductions. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
gen12.1 | ⊢ ( 𝜑 ▶ 𝜓 ) |
Ref | Expression |
---|---|
gen12 | ⊢ ( 𝜑 ▶ ∀𝑥∀𝑦𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gen12.1 | . . . 4 ⊢ ( 𝜑 ▶ 𝜓 ) | |
2 | 1 | in1 37808 | . . 3 ⊢ (𝜑 → 𝜓) |
3 | 2 | alrimivv 1843 | . 2 ⊢ (𝜑 → ∀𝑥∀𝑦𝜓) |
4 | 3 | dfvd1ir 37810 | 1 ⊢ ( 𝜑 ▶ ∀𝑥∀𝑦𝜓 ) |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1473 ( wvd1 37806 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 |
This theorem depends on definitions: df-bi 196 df-vd1 37807 |
This theorem is referenced by: sspwtr 38070 pwtrVD 38081 pwtrrVD 38082 suctrALT2VD 38093 truniALTVD 38136 trintALTVD 38138 suctrALTcfVD 38181 |
Copyright terms: Public domain | W3C validator |