Theorem axfrege52c 44996

Description: Justification for ax-frege52c 44997. (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 3740	. 2 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 ↔ [𝐵 / 𝑥]𝜑))
2	1	biimpd 232	1 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

This proof depends on syntax axioms:   → wi 4   = wceq 1569  [wsbc 3738

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-cleq 2752  df-clel 2835  df-sbc 3739

This theorem is used by: (None)