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Theorem nalequcoms 1480
Description: A commutation rule for distinct variable specifiers. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 2-Feb-2015.)
Hypothesis
Ref Expression
nalequcoms.1 (¬ ∀𝑥 𝑥 = 𝑦𝜑)
Assertion
Ref Expression
nalequcoms (¬ ∀𝑦 𝑦 = 𝑥𝜑)

Proof of Theorem nalequcoms
StepHypRef Expression
1 alequcom 1478 . . 3 (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
21con3i 604 . 2 (¬ ∀𝑦 𝑦 = 𝑥 → ¬ ∀𝑥 𝑥 = 𝑦)
3 nalequcoms.1 . 2 (¬ ∀𝑥 𝑥 = 𝑦𝜑)
42, 3syl 14 1 (¬ ∀𝑦 𝑦 = 𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1312   = wceq 1314
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 586  ax-in2 587  ax-10 1466
This theorem is referenced by:  nd5  1772
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