Theorem aecoms-o 38920

Description: A commutation rule for identical variable specifiers. Version of aecoms 2427 using ax-c11 38905. (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 38919	. 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 1539

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 1968  ax-7 2009  ax-c5 38901  ax-c4 38902  ax-c7 38903  ax-c10 38904  ax-c11 38905  ax-c9 38908

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781

This theorem is referenced by:  hbae-o  38921  dral1-o  38922  dvelimf-o  38947  aev-o  38949  ax12indalem  38963  ax12inda2ALT  38964