Theorem axfrege52c 42628

Description: Justification for ax-frege52c 42629. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
axfrege52c	⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

Proof of Theorem axfrege52c

Step	Hyp	Ref	Expression
1		dfsbcq 3779	. 2 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 ↔ [𝐵 / 𝑥]𝜑))
2	1	biimpd 228	1 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

Syntax hints:   → wi 4   = wceq 1541  [wsbc 3777

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782  df-cleq 2724  df-clel 2810  df-sbc 3778

This theorem is referenced by: (None)