Theorem axfrege52c 44504

Description: Justification for ax-frege52c 44505. (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 3755	. 2 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 ↔ [𝐵 / 𝑥]𝜑))
2	1	biimpd 232	1 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

Syntax hints:   → wi 4   = wceq 1567  [wsbc 3753

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807  df-cleq 2761  df-clel 2844  df-sbc 3754

This theorem is referenced by: (None)