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Theorem mdandyvr14 39795
Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
mdandyvr14.1 (𝜑𝜁)
mdandyvr14.2 (𝜓𝜎)
mdandyvr14.3 (𝜒𝜑)
mdandyvr14.4 (𝜃𝜓)
mdandyvr14.5 (𝜏𝜓)
mdandyvr14.6 (𝜂𝜓)
Assertion
Ref Expression
mdandyvr14 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (𝜂𝜎))

Proof of Theorem mdandyvr14
StepHypRef Expression
1 mdandyvr14.2 . 2 (𝜓𝜎)
2 mdandyvr14.1 . 2 (𝜑𝜁)
3 mdandyvr14.3 . 2 (𝜒𝜑)
4 mdandyvr14.4 . 2 (𝜃𝜓)
5 mdandyvr14.5 . 2 (𝜏𝜓)
6 mdandyvr14.6 . 2 (𝜂𝜓)
71, 2, 3, 4, 5, 6mdandyvr1 39782 1 ((((𝜒𝜁) ∧ (𝜃𝜎)) ∧ (𝜏𝜎)) ∧ (𝜂𝜎))
Colors of variables: wff setvar class
Syntax hints:  wb 195  wa 383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 196  df-an 385
This theorem is referenced by: (None)
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