Theorem aecoms-o 36040

Description: A commutation rule for identical variable specifiers. Version of aecoms 2450 using ax-c11 36025. (Contributed by NM, 10-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
alequcoms-o.1	⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑)

Assertion

Ref	Expression
aecoms-o	⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑)

Proof of Theorem aecoms-o

Step	Hyp	Ref	Expression
1		aecom-o 36039	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
2		alequcoms-o.1	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑)
3	1, 2	syl 17	1 ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-c5 36021  ax-c4 36022  ax-c7 36023  ax-c10 36024  ax-c11 36025  ax-c9 36028

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781

This theorem is referenced by:  hbae-o  36041  dral1-o  36042  dvelimf-o  36067  aev-o  36069  ax12indalem  36083  ax12inda2ALT  36084