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Theorem axc5sp1 34712
Description: A special case of ax-c5 34672 without using ax-c5 34672 or ax-5 1988. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc5sp1 (∀𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥)

Proof of Theorem axc5sp1
StepHypRef Expression
1 equidqe 34711 . 2 ¬ ∀𝑦 ¬ 𝑥 = 𝑥
21pm2.21i 116 1 (∀𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-c7 34674  ax-c10 34675
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854
This theorem is referenced by: (None)
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