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Theorem naecoms 1654
Description: A commutation rule for distinct variable specifiers. (Contributed by NM, 2-Jan-2002.)
Hypothesis
Ref Expression
naecoms.1 (¬ ∀𝑥 𝑥 = 𝑦𝜑)
Assertion
Ref Expression
naecoms (¬ ∀𝑦 𝑦 = 𝑥𝜑)

Proof of Theorem naecoms
StepHypRef Expression
1 ax-10 1437 . . 3 (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
21con3i 595 . 2 (¬ ∀𝑦 𝑦 = 𝑥 → ¬ ∀𝑥 𝑥 = 𝑦)
3 naecoms.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 1283   = wceq 1285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 577  ax-in2 578  ax-10 1437
This theorem is referenced by:  nfcvf2  2245
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