Theorem axfrege52c 38498

Description: Justification for ax-frege52c 38499. (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 3470	. 2 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 ↔ [𝐵 / 𝑥]𝜑))
2	1	biimpd 219	1 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

Syntax hints:   → wi 4   = wceq 1523  [wsbc 3468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-ext 2631

This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745  df-cleq 2644  df-clel 2647  df-sbc 3469

This theorem is referenced by: (None)